This article is cited in 1 paper

Tests for normality of the probabilistic distribution when data are rounded

V. G. Ushakov^ab, N. G. Ushakov<sup>cd

a</sup> Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomo- nosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
^b Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
^c Institute of Microelectronics Technology and High-Purity Materials of the Russian Academy of Sciences, 6 Academician Osipyan Str., Chernogolovka, Moscow Region 142432, Russian Federation
^d Norwegian University of Science and Technology, 15A S. P. Andersensvei, Trondheim 7491, Norway

Abstract: Tests for normality are less sensitive to the data rounding than, for example, tests for exponentiality but among normality tests, the sensitivity is very different. In this paper, the authors find out which tests are more and which ones are less sensitive. The authors show that tests based on sample moments are much more robust with respect to the data rounding than tests based on order statistics (in contrast to the robustness with respect to outliers where order statistics are more robust than sample moments). This, however, only applies to the probability of Type I error. The probability of Type II error is very insensitive to the data rounding for all normality tests.

Keywords: normal distribution, test for normality, rounded data, significance level, Monte-Carlo simulation.

Received: 20.03.2022

DOI: 10.14357/19922264230103